Le funzioni nella scuola secondaria di secondo grado: studio sulle concezioni e sulle conversioni tra registri

To have access to mathematical concepts, students do not refer to their formal definition. Usually when they are solving a mathematical problem or when they are getting new concepts, students refer to some examples of a concept or they refer to the processes in which the concept is involved. Therefore, it's a question of the cognitive schemes linked with the experience that the students have done with that concept. \\ We want to investigate the high student's "images" of function and how these "images" influence the solution processes of different kind of problems. For this purpose a questionnaire has been elaborated. It has been administrated to 323 high school students and the answers have been analysed. The questionnaire is made up by four problems, each of them enables to inquire a particular aspect of the "image" of function of the students. We decided to concentrate on graphs of functions: getting information by a graph and production of graphs with particular features. \\ The questionnaire enables also to inquire the difficulties students meet when they translate a mathematical object from a register of representation to another. \\ In the end, the last question of the questionnaire asks to give a definition of function. \\ After analysing student's answers, we reached two conclusions. \\ The former one deals with difficulties students meet in transforming representations from a register of representation to another: students met more difficulties in transforming representations of a function from graphic register to the verbal one, than in putting into practice the reverse process. \\ The latter conclusion follows: we observed that students mobilized different cognitive schemes to answer different questions. This latter observation suggests that the integration of different "images" of function requires a particular didactic attention.